### Interference and Arrhythmia

Thinking about our way of presenting this material, about problems connected with naturalistic demonstration and having some experience in computer modeling, it was decided to create trustworthy(!) highly precise programs allowing us to observe phenomena without expensive experiments. The programs can be used both for serious investigations and as a visual teaching aid.

There is a lot written about interference, and, at first sight, this important natural phenomenon seems to have been studied completely enough. However, this is far from the case. Let us consider two examples: 1) frequencies of sources are equal; 2) the frequencies are different.

1) Frequencies of Sources Are Equal

To make our discussion more objective, let us refer to figures, depicting standard interference patterns for two coherent oscillators without phase shift:

Fig. 14

For clarity, we simplify the pictures and show only node lines. Let us consider a case, when phase shift of the oscillators is zero for any velocity.

Fig. 15. The sources are coherent. Deformation is obvious.

Appearance of an additional node line indicates deformation of the pattern. Calculation shows that the deformation results in a reaction whose vector is directed to decelerate the motion down to V=0. This is why, in the case of the absence of a phase shift, any inertial motion is out of question - the system will experience continual braking, and what’s more, the higher the velocity, the stronger the braking reaction!

Let us consider another case in which, as velocity increases, the phase shift grows. For the time being, we do not discuss the reason for the phase shift, this is not a simple question, but we can ascertain that the phase difference changes automatically.

Having spent energy increasing the phase difference, we note that an inverse process does not occur and deformation of the interference pattern is absent. Moreover, the braking reaction is absent too, and any attempt to brake the motion causes reaction of another kind called inertia.

Fig. 16. In presence of appropriate phase shift, deformation is absent.

However, what to do, as uniform motion is necessarily connected with phase difference, and phase difference is impossible without motion?

It does not appear to be possible to say what is primary. Most probably, it is a matter of dualism, of indivisible intercommunication. It should, however, be realized, that the conclusions made by us are true only in the case of the presence of a third party - of a real medium! Experience of the previous generation shows, that absence of a specific carrier of waves necessarily leads to confusion of the situation with consequent loss of common understanding.

The most simple and widespread way of obtaining a phase shift in bodies is an external action changing their velocities. If by changing the velocity of a system we change the phase difference, then an inverse effect is possible too: that a phase shift from inside of a system must change its velocity.

2) Frequencies of Sources Are Different

So, we determined that a constant phase shift of oscillators is the only reason for non-violent motion of a system with a constant velocity. Will motion conditions change, if we increase the phase difference continuously, that, in itself, will be seen by us as a change of frequency? However, let us see one after another.

Now, we slightly change the frequency of one of the sources and see what the reaction to the interference field will be:

Fig. 17. V=0. Frequency of the left oscillator is greater than that of the right one.

A wonderful phenomena appears. It has been called the SPIDER-effect because of its resemblance with a spider.

We have already mentioned about a lively standing wave arising in the case of a frequency difference between interacting sources. As a matter of fact, a lively standing wave appears owing to arrhythmia between oscillators which, in turn, causes transfer of energy from the source with the higher frequency to the source with the lower frequency.

We also found a mathematical expression for the velocity of the energy transfer or for the speed of a lively standing wave, which is the same.

Now, it is time to proceed from a one-dimensional consideration to a two-dimensional and then to a three-dimensional one. However, we will not rush and, first, we will consider some properties of a lively standing wave using a one-dimensional model.

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